If your Time Maschine backup volumes filles up you may get a warning message from Time Maschine. It tells you that Time Maschine has deleted the oldest backup set to gain enough space for the actual backup. You can acknowledge the message and even opt to not see it in the future. Time Maschine will then automatically remove oldest backups when needed.
But the deletion of old backups will take some extra time on almost every backup. So maybe you wanna get rid of some old backups manually. This can easily be achieved by starting Time Maschine, navigating to the backup you want to delete and selecting the little gear icon in the Finder. There is an option “Delete Backup”. This will remove this point in time of your backup after asking for your authorization.
If you removed a couple of backup sets to be removed Time Maschine will need some time to wipe all the files. You will see a progress window like when flushing the trash can.
After the clean up you should have enough space for your next couple of backups. You should not delete any files or folders from the backup volume by your self. Time Maschine is doing an intelligent sparse backup. If you delete files or folders manually you may destroy the consistency of your backup and thus make it useless.